An explicit *-product on the cotangent bundle of a Lie group. (English) Zbl 0522.58019

Summary: We give explicit formulas for a *-product on the cotangent bundle \(T^*G\) of a Lie group \(G\); these formulas involve on the one hand the multiplicative structure of the universal enveloping algebra \(U(\mathfrak g)\) of the Lie algebra \(\mathfrak g\) of \(G\) and on the other hand bidifferential operators analogous to the ones used by Moyal to define a *-product on \(\mathbb R^{2n}\).


53D55 Deformation quantization, star products
53B50 Applications of local differential geometry to the sciences
22E46 Semisimple Lie groups and their representations
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